Bose-Einstein condensation of atoms with attractive interaction

We suggest that crucial effect on Bose-Einstein condensation in systems wit h attractive potential is three-body interaction. We investigate stationary solutions of the Gross-Pitaevskii equation with negative scattering length and a higher-order stabilising term in presence of an external parabolic p otential. Stability properties of the condensate are similar to those for t hermodynamic systems in statistical physics which have first order phase tr ansitions. We have shown that there are three possible type of stationary s olutions corresponding to stable, metastable and unstable phases. Results a re discussed in relation to recently observed Li-7 condensate.